Over here, your water bill has 2 components, the price of the fresh water and the price of the waste water. Waste water is at least as expensive per m³ as fresh water, sometimes more than double. If you are using rain water, you save on the fresh water price, but you have to still pay for the waste water. And since waste water price is calculated from your fresh water consumption, you either have to have a second meter for the rain water (expensive) or you pay for an estimated amount of rainwater calculated from the roof area you are collecting from. Also very expensive, because the estimate is always not in your favour.

So not really "free" at all, and rather expensive enough that nobody does it...

This also depends a lot on your locality. If you live in an area where septic tanks are allowed you don't have to pay for city sewer usage.

You can also skip that entirely with a composting toilet. Again depending on your local laws, gray water can often be drained directly outside, potentially through a leech field if required. Plenty of areas allow this for specific uses like washing machines, the only reason it can't be done with standard toilets is because of the solid waste.

Where is here?

Germany

How does the water company know you're using rain water?

They don't. It's just verboten to do it without reporting it, and if they catch you there will be Konsequenzen!